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We review briefly several of the current major areas of application to chemistry. The topics covered include chemical documentation, isomer enumeration, chemical bonding theory, the study of chemical reaction networks, planning synthesis routes, macromolecules and polymers, and the use of graph invariants (so-called topological indices) for the description and prediction of chemical behavior. The latter topic is treated more fully in the paper immediately following this one. Where appropriate, the contributions of mathematicians, especially graph theorists, to the development of chemical graph theory have been highlighted. A number of the problems of a graph-theoretical nature which still confront the chemist are outlined. Key references to the relevant chemical literature are given, and all the major reviews in the field are cited. Graph theorists desirous of learning more about the chemical applications of their discipline may find the present elementary introduction a convenient point from which to start. Keywords: Graph Theory, Chemistry, Topological Indices, Isomer Enumeration.

We review briefly several of the current major areas of application to chemistry. The topics covered include chemical documentation, isomer enumeration, chemical bonding theory, the study of chemical reaction networks, planning synthesis routes, macromolecules and polymers, and the use of graph invariants (so-called topological indices) for the description and prediction of chemical behavior. The latter topic is treated more fully in the paper immediately following this one. Where appropriate, the contributions of mathematicians, especially graph theorists, to the development of chemical graph theory have been highlighted. A number of the problems of a graph-theoretical nature which still confront the chemist are outlined. Key references to the relevant chemical literature are given, and all the major reviews in the field are cited. Graph theorists desirous of learning more about the chemical applications of their discipline may find the present elementary introduction a convenient point from which to start. Keywords: Graph Theory, Chemistry, Topological Indices, Isomer Enumeration.

We review briefly several of the current major areas of application to chemistry. The topics covered include chemical documentation, isomer enumeration, chemical bonding theory, the study of chemical reaction networks, planning synthesis routes, macromolecules and polymers, and the use of graph invariants (so-called topological indices) for the description and prediction of chemical behavior. The latter topic is treated more fully in the paper immediately following this one. Where appropriate, the contributions of mathematicians, especially graph theorists, to the development of chemical graph theory have been highlighted. A number of the problems of a graph-theoretical nature which still confront the chemist are outlined. Key references to the relevant chemical literature are given, and all the major reviews in the field are cited. Graph theorists desirous of learning more about the chemical applications of their discipline may find the present elementary introduction a convenient point from which to start. Keywords: Graph Theory, Chemistry, Topological Indices, Isomer Enumeration.

We review briefly several of the current major areas of application to chemistry. The topics covered include chemical documentation, isomer enumeration, chemical bonding theory, the study of chemical reaction networks, planning synthesis routes, macromolecules and polymers, and the use of graph invariants (so-called topological indices) for the description and prediction of chemical behavior. The latter topic is treated more fully in the paper immediately following this one. Where appropriate, the contributions of mathematicians, especially graph theorists, to the development of chemical graph theory have been highlighted. A number of the problems of a graph-theoretical nature which still confront the chemist are outlined. Key references to the relevant chemical literature are given, and all the major reviews in the field are cited. Graph theorists desirous of learning more about the chemical applications of their discipline may find the present elementary introduction a convenient point from which to start. Keywords: Graph Theory, Chemistry, Topological Indices, Isomer Enumeration.

We review briefly several of the current major areas of application to chemistry. The topics covered include chemical documentation, isomer enumeration, chemical bonding theory, the study of chemical reaction networks, planning synthesis routes, macromolecules and polymers, and the use of graph invariants (so-called topological indices) for the description and prediction of chemical behavior. The latter topic is treated more fully in the paper immediately following this one. Where appropriate, the contributions of mathematicians, especially graph theorists, to the development of chemical graph theory have been highlighted. A number of the problems of a graph-theoretical nature which still confront the chemist are outlined. Key references to the relevant chemical literature are given, and all the major reviews in the field are cited. Graph theorists desirous of learning more about the chemical applications of their discipline may find the present elementary introduction a convenient point from which to start. Keywords: Graph Theory, Chemistry, Topological Indices, Isomer Enumeration.

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The graph theory derived model for the bonding topology in the globally delocalized polyhedral boranes B6H6(2-) is evaluated by comparison of the energies of the core molecular orbitals with those obtained by the 1962 LCAO-MO extended Huckel calculations of Hoffmann and Lipscomb. Of particular interest is how well the complete graphs K sub 6 and K sub 12 used in the graph theory derived model approximate the bonding topologies of the unique internal orbital (radial orbitals) of the octahedron and icosahedron, respectively. In the case of the B6H6(2-) octahedron the single positive eigenvalue of the K sub 6 graph corresponds to the results from the extended Huckel calculations. In the case of the B12H12(2-) icosahedron the graph theory derived model is far less satisfactory since the singl positive eigenvalue of the K sub 12 graph disagrees with the four bonding core molecular orbitals (an A1g and three triply degenerate T sub 1u molecular orbitals) found by the extended Huckel calculations after removing the effect of the mixing of core and surface bonding orbitals corresponding to the same irreducible representations. However, this core-surface orbital mixing raises the energy of the triply degenerate T sub 1u core molecular orbitals to antibonding levels so that the graph theory derived model fortuitiously gives correct skeletal electron counts for the regular icosahedron despite this fundamental error.